Problem: The grades on a language midterm at Springer are normally distributed with $\mu = 72$ and $\sigma = 4.5$. Daniel earned a $65$ on the exam. Find the z-score for Daniel's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Daniel's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{65 - {72}}{{4.5}}} $ ${ z \approx -1.56}$ The z-score is $-1.56$. In other words, Daniel's score was $1.56$ standard deviations below the mean.